Ultra-efficient and parameter-free computation of submicron thermal transport with phonon Boltzmann transport equation.

Understanding thermal transport at the submicron scale is crucial for engineering applications, especially in the thermal management of electronics and tailoring the thermal conductivity of thermoelectric materials. At the submicron scale, the macroscopic heat diffusion equation is no longer valid and the phonon Boltzmann transport equation (BTE) becomes the governing equation for thermal transport. However, previous thermal simulations based on the phonon BTE have two main limitations: relying on empirical parameters and prohibitive computational costs. Therefore, the phonon BTE is commonly used for qualitatively studying the non-Fourier thermal transport phenomena of toy problems. In this work, we demonstrate an ultra-efficient and parameter-free computational method of the phonon BTE to achieve quantitatively accurate thermal simulation for realistic materials and devices. By properly integrating the phonon properties from first-principles calculations, our method does not rely on empirical material properties input. It can be generally applicable for different materials and the predicted results can match well with experimental results. Moreover, by developing a suitable ensemble of advanced numerical algorithms, our method exhibits superior numerical efficiency. The full-scale (from ballistic to diffusive) thermal simulation of a 3-dimensional fin field-effect transistor with 13 million degrees of freedom, which is prohibitive for existing phonon BTE solvers even on supercomputers, can now be completed within two hours on a single personal computer. Our method makes it possible to achieve the predictive design of realistic nanostructures for the desired thermal conductivity. It also enables accurately resolving the temperature profiles at the transistor level, which helps in better understanding the self-heating effect of electronics.

GiftBTE: an efficient deterministic solver for non-gray phonon Boltzmann transport equation.

Advances in nanotechnology have facilitated the exploration of submicron thermal transport. At this scale, Fourier's law is no longer applicable, and the governing equation for thermal transport is the phonon Boltzmann transport equation (BTE). However, the availability of open-source solvers for the phonon BTE is limited, impeding progress in this field. This study introduces an open-source package, GiftBTE, for numerically solving the non-gray phonon BTE. GiftBTE employs deterministic solutions and provides both steady-state and transient solvers. For the steady-state solver, GiftBTE employs the implicit discrete ordinates method (DOM) with second-order spatial accuracy and the synthetic iterative scheme. For the transient solver, GiftBTE employs the explicit DOM with second-order spatial accuracy. This package demonstrates excellent computational efficiency, enabling realistic three-dimensional simulations of devices and materials. By interfacing with first-principles calculations, this solver enables parameter-free computation of submicron thermal transport. The application of GiftBTE includes, but is not limited to, computing the thermal conductivity of nanostructures, predicting temperature rises in transistors, and simulating laser heating processes.

Simulating and interpreting Kelvin probe force microscopy images on dielectrics with boundary integral equations.

Kelvin probe force microscopy (KPFM) is designed for measuring the tip-sample contact potential differences by probing the sample surface, measuring the electrostatic interaction, and adjusting a feedback circuit. However, for the case of a dielectric (insulating) sample, the contact potential difference may be ill defined, and the KPFM probe may be sensing electrostatic interactions with a certain distribution of sample trapped charges or dipoles, leading to difficulty in interpreting the images. We have proposed a general framework based on boundary integral equations for simulating the KPFM image based on the knowledge about the sample charge distributions (forward problem) and a deconvolution algorithm solving for the trapped charges on the surface from an image (inverse problem). The forward problem is a classical potential problem, which can be efficiently solved using the boundary element method. Nevertheless, the inverse problem is ill posed due to data incompleteness. For some special cases, we have developed deconvolution algorithms based on the forward problem solution. As an example, this algorithm is applied to process the KPFM image of a gadolinia-doped ceria thin film to solve for its surface charge density, which is a more relevant quantity for samples of this kind than the contact potential difference (normally only defined for conductive samples) values contained in the raw image.

A resolution study for electrostatic force microscopy on bimetallic samples using the boundary element method.

Electrostatic force microscopy (EFM) is a special design of non-contact atomic force microscopy used for detecting electrostatic interactions between the probe tip and the sample. Its resolution is limited by the finite probe size and the long-range characteristics of electrostatic forces. Therefore, quantitative analysis is crucial to understanding the relationship between the actual local surface potential distribution and the quantities obtained from EFM measurements. To study EFM measurements on bimetallic samples with surface potential inhomogeneities as a special case, we have simulated such measurements using the boundary element method and calculated the force component and force gradient component that would be measured by amplitude modulation (AM) EFM and frequency modulation (FM) EFM, respectively. Such analyses have been performed for inhomogeneities of various shapes and sizes, for different tip-sample separations and tip geometries, for different applied voltages, and for different media (e.g., vacuum or water) in which the experiment is performed. For a sample with a surface potential discontinuity, the FM-EFM resolution expression agrees with the literature; however, the simulation for AM-EFM suggests the existence of an optimal tip radius of curvature in terms of resolution. On the other hand, for samples with strip- and disk-shaped surface potential inhomogeneities, we have obtained quantitative expressions for the detectability size requirements as a function of experimental conditions for both AM- and FM-EFMs, which suggest that a larger tip radius of curvature is moderately favored for detecting the presence of such inhomogeneities.